
Journal of Lie Theory 30 (2020), No. 2, 361370 Copyright Heldermann Verlag 2020 Curvature of Matrix and Reductive Lie Groups Luyining Gan Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, U.S.A. lzg0027@auburn.edu Ming Liao Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, U.S.A. liaomin@auburn.edu TinYau Tam Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557, U.S.A. ttam@unr.edu We give a simple formula for sectional curvatures on the general linear group, which is also valid for many other matrix groups. Similar formula is given for a reductive Lie group. We also discuss the relation between commuting matrices and zero sectional curvature. Keywords: Curvature, general linear group, reductive Lie group, closed subgroup. MSC: 53B20, 14L35, 51N30. [ Fulltextpdf (110 KB)] for subscribers only. 